Slim models of Zermelo set theory
AbstractWorking in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence ⟨Aλ ∣ λ a limit ordinal⟩ where for each λ. Aλ ⊆ λ2, there is a supertransitive inner model of Zermelo containing all ordinals in which for every λAλ = {a ∣ Φ(λ, a)}.
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2006 ◽
Vol 71
(4)
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pp. 1200-1222
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1972 ◽
Vol 6
(3)
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pp. 447-457
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2020 ◽
Vol 476
(2239)
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pp. 20190782
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